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This paper presents a balanced truncation technique for model and scheduling order-reduction (i.e. reduction of number of states as well as of scheduling parameters) of exponentially stable temporal- and spatial-LPV interconnected systems. The reduction is based on the application of the full block S-procedure, using both Constant Gramians (CGs) and Parameter-Dependent Gramians (PDGs). The reduced...
Novel stability and quadratic performance conditions in LMI form are presented that allow the design of fixed-structure controllers for linear time-space-invariant spatially interconnected systems in input-output form. By using an implicit distributed input-output representation, Finsler's Lemma can be applied, while avoiding issues resulting from non-causality of spatially interconnected systems...
This paper presents a two-step distributed antiwindup (AW) design for spatially-interconnected systems. Analogous to the distributed controller design, the AW compensator also reflects the distributed nature of the controlled system. A lumped AW scheme is extended here to spatially-interconnected systems. The nonlinear saturation operator can be characterized in a quadratic form using a suitable multiplier...
In this paper, the synthesis of a network of local controllers for the purpose of controlling the transition from laminar to turbulent flow is presented, using a recently proposed spatially interconnected model of plane Poiseuille flow. Measured feedback signals used by the controllers are the local changes in wall shear force, and the generated control action is a local change in fluid wall normal...
This paper presents a case study on distributed controller design for spatially-invariant and linear parameter-varying (LPV) models. To apply recently proposed state-space-based synthesis conditions, the experimentally identified input/output models are realized in terms of multidimensional state space representations, both for spatially-invariant and LPV models. Inheriting the interconnected structure...
This paper considers the application of Finsler's Lemma to the synthesis of LPV controllers when dependence on scheduling parameters is affine or rational with a certain structure. With a view on established LPV synthesis techniques, we propose solutions to preserve affine parameter dependence of linear matrix inequality conditions and thus facilitate controller synthesis. The proposed methods are...
The notion of output-feedback controlled-invariant sets is extended from LTI systems to systems with linear parameter-varying state transition matrix. A theorem is presented that can be used to verify whether a given polytope can be made invariant under output-feedback. The theorem also provides the constraints a control input has to fulfill to make the candidate set invariant. Predictive output-feedback...
In this paper, observer-based linear parameter-varying (LPV) control of the one-dimensional nonlinear Burgers' equation is presented. The partial differential equation is discretized using a finite difference scheme and the boundary conditions are taken as control inputs. A nonlinear high-order state space model is generated and proper orthogonal decomposition based Galerkin projection is used for...
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